The threshold of audibility of phase noise in ADC and DAC clocks is a fairly contentious issue in the HiFi and audiophile world. Some sources claim that jitter is clearly audible at low levels, and some claim that high levels of jitter are inaudible. The literature describes several tests, many with conflicting results.

One of the chief difficulties in testing the audibility of jitter is that it requires a complex hardware setup, which means that many listeners would be required to be present for an time consuming (and expensive) on site test. Over the last couple of months I have been thinking about organising a distributed listening test to look at the audibility of jitter in audio applications, based on algorithms for simulating the effects of jitter on signals. These algorithms are fairly well described in RF and telecomms engineering literature, and would be interesting for comparison purposes.

The kind of thing I have in mind is this:Use samples which are accepted to sound good -> simulate jitter -> perform listening tests -> perform more tests at different levels of jitter depending on results

The purpose of this thread is to get ideas of the Hydrogenaudio community about performing these tests. Some of the things I would appreciate input on are:

John, the post that you quote refers specifically to RANDOM jitter. How can this possibly produce anything remotely resembling a 3 kHz tone?

Thanks for the correction - I failed to note that their paper was confined to random jitter. The distortion caused by this random jitter should be much less audible than the distortion caused by siusoidal jitter.

To reach audibility, the distortion caused by random jitter may need to be 20 to 30 dB higher than the distortion caused by sinusoidal jitter.

The "random jitter" used in this experiment is frequency limited by the Nyquist theorem. Consequently, the jitter-induced distortion will have nearly the same spectral shape as the jitter. If the spectrum of the band-limited random jitter is white, we should expect the spectrum of the jitter-induced distortion to be nearly white. TPDF dither noise will be very effective at masking this spectrally-white jitter-induced distortion. If the jitter-induced distortion is the same amplitude as 16-bit TPDF dither noise, the system noise level will increase by 3 dB. If the jitter-induced distortion is 6 dB lower than the 16-bit TPDF noise, system noise will increase by 1 dB. In this experiment, the jitter-induced distortion is simply a white noise signal that gets added to the system noise.

Note: Use RMS noise summing equations to calculate resulting noise.

Digital audio transmission systems tend to generate jitter at very specific frequencies. The spectrum of the code-induced jitter at the end of a S/PIF cable is much closer to sinusoidal than random. Spectrally white random jitter is not likely to occur in the real world. Jitter composed one or two dominant sinusoidal frequencies is much more common. In my opinion it is more important to investigate the audibility thresholds for sinusoidal jitter.

Obviously the investigation of random jitter is a good first step as it requires far fewer tests than an investigation of random jitter. With random jitter we have one variable - amplitude. An investigation of sinusoidal jitter would require two variables - amplitude and frequency. Many tests would be required to plot the audibility curves.

We should be able to estimate the audibility of sinusoidal jitter-induced distortion using masking theory. Has anyone published these calculations?

We should be able to estimate the audibility of sinusoidal jitter-induced distortion using masking theory. Has anyone published these calculations?

Are there any good papers on the audibility of sinusoidal jitter?

Julian Dunn calculated the audibility threshold of jitter-induced sidebands produced by sinusoidal jitter. He took making effects into account when calculating audibility. His calculations are based upon a peak playback level of 120dB SPL and he assumes that un-masked sidebands become audible at 0 dB SPL.

Peak playback levels are usually lower than 120 dB SPL, and audibility thresholds will usually be slightly higher than 0 dB SPL (due to ambient noise), so his jitter-audibility plot is a worst-case audibility plot. These results could be scaled for other playback levels and ambient noise levels.

See section 3.3 for an explanation, and figure 9 for a plot of "maximum inaudible jitter amplitude" vs frequency.

In summary of Julian Dunn's calculations: 1us at jitter frequencies below 200 Hz should be inaudible1ns at a jitter-frequency of 600 Hz should be inaudible100 ps at a jitter-frequency of about 3 kHz should be inaudible20 ps a jitter-frequency of 20 kHz should be inaudible

A detailed paper on the derivation of theses numbers can be found here:

His calculations are based upon a peak playback level of 120dB SPL and he assumes that un-masked sidebands become audible at 0 dB SPL.

Can I explain this in suitably scientific language?

It's taking the Michael.

QUOTE

See section 3.3 for an explanation, and figure 9 for a plot of "maximum inaudible jitter amplitude" vs frequency.

In summary of Julian Dunn's calculations: 1us at jitter frequencies below 200 Hz should be inaudible1ns at a jitter-frequency of 600 Hz should be inaudible100 ps at a jitter-frequency of about 3 kHz should be inaudible20 ps a jitter-frequency of 20 kHz should be inaudible

So you need less than 20ps jitter - otherwise, when you play back 20kHz sine wave at 120dB SPL, the jitter-induced noise might have a total power equivalent to 0dB SPL.

QUOTE

A detailed paper on the derivation of theses numbers can be found here:

His calculations are based upon a peak playback level of 120dB SPL and he assumes that un-masked sidebands become audible at 0 dB SPL.

Can I explain this in suitably scientific language?

It's taking the Michael.

QUOTE

See section 3.3 for an explanation, and figure 9 for a plot of "maximum inaudible jitter amplitude" vs frequency.

In summary of Julian Dunn's calculations: 1us at jitter frequencies below 200 Hz should be inaudible1ns at a jitter-frequency of 600 Hz should be inaudible100 ps at a jitter-frequency of about 3 kHz should be inaudible20 ps a jitter-frequency of 20 kHz should be inaudible

So you need less than 20ps jitter - otherwise, when you play back 20kHz sine wave at 120dB SPL, the jitter-induced noise might have a total power equivalent to 0dB SPL.

The first fallacy here is the idea that the human threshold of hearing remains at 0 dB while a human is listening to 20 Hz at 120 dB. IOW, there is a presumption that theshold shifts never happen, even in the presence of 120 dB sounds.

The second fallacy is that there would ever be a natural sound that is a 120 dB 20 Hz pure tone with all other sounds 120 dB down.

The third fallacy is that there is anybody actually listens to reproduced sound in a context where the listening environment's residual noise is at 0 dB or below, other than as part of a lab esperiment.